The quartz micro electro mechanical system (MEMS) gyroscope is a kind of Coriolis vibrating gyros. Its sensitive chip adopts a tuning fork structure, which is in a resonant state during operation. The sensitive chip has multiple modes, and the first nine modes cover the frequency from 3 kHz to 21 kHz. Some modes of the sensitive chip are susceptible to the external vibration, which causes the sensitive chip to resonate and resulting in zero offset error of gyro. The zero offset error of gyro can reach 0.5 (°)/s. In this paper, the mechanism of the modal resonance error of the sensitive chip is analyzed, and proposes a stagger frequency design in structure to avoid the influence of external specific frequency on the sensitive chip, so as to suppress the zero offset error. The zero offset error is reduced to about 0.03 (°)/s, and the adaptability of the gyro to the vibration environment is improved.